# The Mortar Method in the Wavelet Context

Silvia Bertoluzza; Valérie Perrier

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 35, Issue: 4, page 647-673
- ISSN: 0764-583X

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topBertoluzza, Silvia, and Perrier, Valérie. "The Mortar Method in the Wavelet Context." ESAIM: Mathematical Modelling and Numerical Analysis 35.4 (2010): 647-673. <http://eudml.org/doc/197416>.

@article{Bertoluzza2010,

abstract = {
This paper deals with the use of wavelets in the framework of the Mortar method.
We first review in an abstract framework the theory of the mortar method for
non conforming domain decomposition, and point out some basic assumptions
under which stability and convergence of such method can be proven. We study
the application of the mortar method in the biorthogonal wavelet framework.
In particular we define suitable multiplier spaces for imposing weak
continuity. Unlike in the classical mortar method, such multiplier spaces are
not a subset of the space of traces of interior functions, but rather of
their duals.
For the resulting method, we provide with an error estimate, which is optimal in the
geometrically conforming case.
},

author = {Bertoluzza, Silvia, Perrier, Valérie},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Domain decomposition; mortar method; wavelet approximation.; domain decomposition; wavelet approximation; stability; convergence; error estimate},

language = {eng},

month = {3},

number = {4},

pages = {647-673},

publisher = {EDP Sciences},

title = {The Mortar Method in the Wavelet Context},

url = {http://eudml.org/doc/197416},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Bertoluzza, Silvia

AU - Perrier, Valérie

TI - The Mortar Method in the Wavelet Context

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 4

SP - 647

EP - 673

AB -
This paper deals with the use of wavelets in the framework of the Mortar method.
We first review in an abstract framework the theory of the mortar method for
non conforming domain decomposition, and point out some basic assumptions
under which stability and convergence of such method can be proven. We study
the application of the mortar method in the biorthogonal wavelet framework.
In particular we define suitable multiplier spaces for imposing weak
continuity. Unlike in the classical mortar method, such multiplier spaces are
not a subset of the space of traces of interior functions, but rather of
their duals.
For the resulting method, we provide with an error estimate, which is optimal in the
geometrically conforming case.

LA - eng

KW - Domain decomposition; mortar method; wavelet approximation.; domain decomposition; wavelet approximation; stability; convergence; error estimate

UR - http://eudml.org/doc/197416

ER -

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- Christine Bernardi, Frédéric Hecht, Olivier Pironneau, Coupling Darcy and Stokes equations for porous media with cracks
- Christine Bernardi, Frédéric Hecht, Olivier Pironneau, Coupling Darcy and Stokes equations for porous media with cracks

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